Answer to Question #289738 in Statistics and Probability for GOAT

Question

Given a die it has 6 faces in which gas either dot of x = 1, 2,3, 4, 5,6. Consider the sample of size n= 3. Illustrate the sampling distrubution and the central limit theorem.

Answer 1

The average of three dice is taken as the sample mean of all sample and the results of 30 sample means are plotted on the frequency curve and it represents a normal distribution.

As per central limit theorem,

The sample means follow normal distribution as can be seen from the relative frequency curve.

If number of samples will be increased from 30 to larger number then the curve would perfectly fit normal distribution.